(g) Summarize what you have learned from this simulation. In particular,

  • Describe the shape, center, and variability (with appropriate numerical support) of this null distribution.
  • This null distribution should center around zero. Verify and then explain why.
  • Where does the difference in sample means (unrestricted group - deprived group) observed by these researchers fall in this null distribution (near the middle or in a tail)? Is such an outcome surprising when the null hypothesis is true? Enough for you to reject the null hypothesis? How are you deciding?
  • Calculate a standardized statistic by taking the observed statistic minus the mean specified by the null hypothesis, and then dividing by your estimate of the standard error of the statistic (the standard deviation of the null distribution). Show the details of your calculation and interpret your result.
  • Interpret the estimated p-value in your own words: If we repeatedly ....
    (Don't simply decide whether it's small, but explain what it measures: The proportion of whats that do what assuming what?)

(h) Informal confidence interval: Use the observed statistic and two times the standard deviation from your null distribution to approximate a 95% confidence interval for the parameter: statistic + 2xSE. Show the details of your calculation and report your interval in context.


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